The enormous increase in the recording density of a hard disk has mainly been achieved by scaling the dimensions of the bits recorded in the storage layer. The capacity of the data recording density is characterized by the magnetocrystalline anisotropy energy (MAE). Hence, controlling or manipulating the magnetocrystalline anisotropies in thin films and multilayers^[1,2] is attractive technologically. Moreover, the MAE is fundamentally interesting, because of the interplay among charge, spin and lattice structure in the interface and surface. Several decades ago, Bruno^[3] first proposed that the MAE is proportional to the expectation value of the orbit moment. Although the proposition was later corroborated by Weller et al.,^[4] the model is not suitable for all situations. In 1999, Gerrit van der Laan derived that the MAE is directly related to the anisotropic part of the spin–orbit interaction, rather than to the orbital part of the magnetic moment. Meanwhile, he also demonstrated that the sum and weighted difference signals over the L₂ and L₃ edges in the x-ray magnetic linear dichroism (XMLD) spectrum are proportional to the anisotropy in the charge distribution and spin–orbit interaction, respectively.^[5] The anisotropy spin–orbit interaction, which can be extracted from data measured by XMLD, is related to the MAE. Therefore the XMLD can be used as a valuable tool to measure the MAE of thin films and multiplayers.^[6,7] Fe_xCo_{1 − x} alloy is one of Heusler alloy compounds which were extensively studied. The orbital moment and MAE of Co have maxima when x is around 0.6, i.e., x ∼ 0.6.^[8–10] Some reports showed that the MAE of Fe–Co alloy is about 100 μeV/atom–200 μeV/atom,^[11] or even up to 700 μeV/atom–800 μeV/atom.^[12] In the present work, we report the effect of the sample thickness on the surface MAE of Co₃₃Fe₆₇ films using the XMLD method.

Alloy films with different thickness (5, 20, 50, 71, and 95 nm) were prepared on Si (100) substrates by DC magnetron sputtering at room temperature. Single composite targets containing 67% Fe and 33% Co were used. The base pressure of the chamber was below 1× 10^{− 3} Pa, and the sputtering pressure of argon was 0.13 Pa. The film depositing rate was controlled to be about 1 Å/s. After deposition, films were capped with 3.5 nm Ta to prevent it from oxidizing. XMLD experiments were carried out at 3W1B^[11] beamline of Beijing Synchrotron Radiation Facility (BSRF). The degree of linear polarization of the beam used was about 92%. A planar grating monochromator was used to generate soft x-ray in an energy range of 50 eV–1500 eV which covers L_2,3 edges of 3d transmission metals. The saturation magnetization field was typically about 300 Oe (1 Oe=79.5775 A·m⁻¹) for those alloy films. And thus the external field provided by a pair of permanent magnets was about 4000 Oe that enabled those samples to be magnetized to the saturated states. During the measurements, the polarization plane of incident light and the sample are fixed. At each energy point, the direction of magnetization was continuously rotated so as to be parallel or perpendicular to the polarization plane of incident light. The x-ray absorption spectra (XAS) and XMLD spectra of alloy films recorded in total electron yield (TEY) mode. The results for Co and Fe are shown in Figs. 1 and 2, respectively.

Fig. 1.

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	Fig. 1. (a) Co L2,3 x-ray absorption spectra for the 5-nm film when the direction of magnetization is parallel (red line) and perpendicular (black line) to the polarization plane of incident light. (b)–(f) Co edge XMLD spectra (black line) and the corresponding calculated results (red line) of alloy films in a thickness range from 5 nm to 95 nm.

Fig. 2.

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	Fig. 2. (a) Fe L2,3 x-ray absorption spectra for the 5-nm film when the direction of magnetization is parallel (red line) and perpendicular (black line) to the polarization plane of incident light. (b)–(f) Fe edge XMLD spectra (black line) and the corresponding calculated results (red line) of alloy films in a thickness range from 5 nm to 95 nm.

The MAEs can be extracted from the XMLD and XAS spectra using the following procedure. All XAS are normalized at L₃ peak. The background is subtracted from the XAS in order to isolate the contributions of the 2p → 3d transitions for Co and Fe absorption spectra. In the present study, we use a two-step-like function background to account for non-resonant absorption as reported in Ref. [13]. Some integral quantities coming from sum rules are needed. ΔI_L3 + ΔI_L2 denotes the integrated XMLD signal. I_‖ + I_⊥ = (I_L3‖ + I_L2‖) + (I_L3⊥ + I_L2⊥) is the integrated XAS signal of L edges.^[5,6] These integrals can be calculated by integrating over the L₃ or L₂ edge of XAS and XMLD spectra obtained under corresponding parallel (‖) or perpendicular (⊥) experimental condition. The ratios (ΔI_L3 + ΔI_L2) / (I_‖ + I_⊥) of Co and Fe in different samples are listed in Table 1. The integrated XMLD signals account for about 0.01%∼ 0.04%, indicating that there is no change in the charge anisotropy when the magnetic field direction changes.

Table 1.

Table 1.

Table 1. Ratios (ΔIL3 + ΔIL2) / (I‖ + I⊥) for Co and Fe in Co33Fe67 alloy films with different thickness. . Ratio Element 5 nm 20 nm 50 nm 71 nm 95 nm (ΔIL3 + Δ IL2) / (I‖ + I⊥) Fe 0.01% 0.03% 0.02% 0.04% 0.02% Co 0.04% 0.02% 0.03% 0.02% 0.01%

Table 1. Ratios (ΔIL3 + ΔIL2) / (I‖ + I⊥) for Co and Fe in Co33Fe67 alloy films with different thickness. .

According to the XMLD sum rules, we use the following equations to calculate MAE (ΔE):^[5,6,14,15]

Fig. 3.

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	Fig. 3. Variations of MAE value and exchange field with thickness for Fe (black diamond dot) and Co (red circle dot) of Fe33Co67 alloy films. Black empty diamond dots and red empty circles denote the exchange field values of Fe and Co respectively. Lines are guides for eyes.

Because the probing depths of total electron yield of soft x-ray absorption experiments of Fe and Co metals are both about 40 Å.^[18] These MAE values reflect the surface magnetisms of samples. To identify the physical mechanisms, we need to resort to quantitative explanations of the XMLD spectra. We perform a simulation of the XMLD spectra of Co and Fe using the ligand field multiplet (LFM) model and compared with the spectra.^[13,19–21] LFM calculations as shown in Fig. 1 are performed by using the CTM4XAS 5.2 program, including spin–orbit couplings, crystal field effects, exchange fields and reductions of the Slater integrals F(dd), F(pd), and G(pd) to include the interatomic configuration interaction.^[22,23] The simulations cover the L₃ edge, and some differences appear in L₂ edge, especially for Co, since the 3d bands are delocalized. When the film is thicker, the difference is more obvious. That is because the experiment XMLD signal is small. The following parameters are obtained by comparing the calculated spectra with the experimental spectra: 2p and 3d spin–orbit interactions, which are reduced by being multiplied by factors of 0.82 and 0.80, respectively, for the cobalt cations, while factors of 1.0 and 0.8 are used for iron cations. The Slater integrals F(dd), F(pd), and G(pd) are taken to be 40%, 60%, and 80% of the Hartree–Fock values, respectively, for the cobalt cations, and 40%, 100%, and 80%, respectively, for the iron cations. The crystal field splittings of samples with different thickness are slightly different, which are just 0.02 eV–0.03 eV between the 5-nm-thick film and 95-nm-thick film for Co and Fe. The most obvious difference is the exchange field parameter. In particular, for both Co and Fe, the exchange field values are both about 0.1 eV for 5-nm-thick film and about 0.03 eV for 95-nm-thick film, respectively. From the simulation, it shows that the crystal field splitting plays a trivial role and the exchange field plays an important role in the shape and magnitude of L₃ edge of XMLD spectra. Furthermore, as shown in Fig. 3, the variations of both MAE value and exchange field parameter with thickness are similar, which suggests that they have some close relations.

The exchange field related to the interatomic exchange interaction in 3d metal can be treated as a magnetic field acting only on spin S. It is included by a term gμ_BHS in the Hamiltonian. This field lifts the degeneracy, making the energy of the M_J sublevels equal to −gμ_BHM_J. When exchange interaction is of the same order of magnitude as the spin–orbit interaction (ζ = 50 meV), the different J levels are strongly mixed.^[14] Form the XMLD spectrum calculation parameters, the value of the exchange field is 0.1 eV for 5 nm which is larger than that of 0.03 eV for 95 nm. It suggests that the thinner film gives an enhancement of the spin moment. The exchange field versus thickness and MAE versus the thickness have the same variation tendencies, which reveals the reason why different electron exchange fields leading to different MAE values may relate to the electron structure. Kuneš et al.^[24] and Oppeneer et al.^[25] derived that the XMLD spectrum is proportional to the energy derivative of the exchange polarization of the unoccupied 3d-density of states. Hence, the different magnitudes of XMLD in L₃ edge measured in the present work lead to the redistribution of 3d states in the vicinity of Fermi energy.

In addition, magnetocrystalline anisotropy is expected to change as the symmetry of atoms changes. Usually, the effective anisotropy constant K is used to describe anisotropy. The MAE is proportional to the K. The K is expressed as^[26]

Fig. 4.

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	Fig. 4. Comparisons among the plots of normalization values of Fe MAE (black diamond dot), Co MAE (red circle dot), and the first term of K (blue triangle dot) versus thickness. Lines are guides for eyes.

In this work, we find that the XMLD sum rule is applicable due to the large sensitivity of spin–orbit anisotropy to MAE and we use the XMLD to calculate the element-specific MAE values on surfaces of Co₃₃Fe₆₇ alloy films with different thicknesses. From the XAS and XMLD spectra and sum rules, the integrated XMLD signal is nearly zero. It is evident that the anisotropy arises from the magnetism while there is no contribution from the charge anisotropy. From the MAE calculations, firstly, we find that the MAE values decrease with the increase of the film thickness for both Co and Fe elements. Secondly, the differences in L₃ edge of XMLD indicate the redistribution of 3d states near Fermi level. The most important result is that the variation tendency of exchange field parameter with sample thickness is the same as that of MAE versus sample thickness. It implies that there is a close relationship between them. By comparing with the anisotropy constant K, the reason for different MAE values may result from two causes. Besides thickness effect, the shape anisotropy relating to the interface roughness plays an important role in the thickness dependence on the surface MAE of film. These two factors cause redistribution of 3d electron states to change the absorption atom local circumvent and bring about the variable field felt by itself, which produces different spin–orbit interaction anisotropies, viz. different MAE values.